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New optimization method for steered fiber composites using the level set method

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Abstract

Advanced fiber placement (AFP) composite manufacturing technology offers a means to tailor composite fibers for complex loading environments and significantly improve the overall structural efficiency. This paper introduces a new method to optimize the continuously varying fiber paths for AFP using a level set method. The paths of the fibers are defined by constant level set function values, describing a series of continuous equally spaced fiber paths. The sensitivity of the structural compliance to a change in level set function definition of the fiber path is derived. The sensitivities are used to optimize the level set defined fiber paths to minimize structural compliance, while maintaining the continuous fiber paths and producing a solution that can be manufactured using AFP. The optimization method is demonstrated in three numerical studies.

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References

  • Abdalla MM, Setoodeh S, Gürdal Z (2007) Design of variable stiffness composite panels for maximum fundamental frequency using lamination parameters. Compos Struct 81(2):283–291

    Article  Google Scholar 

  • Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level set method. Comput Phys 194(1):363–393

    Article  MATH  MathSciNet  Google Scholar 

  • Antonio CAC (2006) A hierarchical genetic algorithm with age structure for multimodal optimal design of hybrid composites. Struct Multidiscip Optim 31(4):280–294

    Article  Google Scholar 

  • Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer

  • Bruyneel M (2011) SFP—a new parameterization based on shape functions for optimal material selection: application to conventional composite plies. Struct Multidiscip Optim 43(1):17–27

    Article  Google Scholar 

  • Diaz A, Bendsøe M (1992) Shape optimization of structures for multiple loading conditions using a homogenization method. Sturct Optim 4(1):17–22

  • Dunning PD, Kim HA (2011) Investigation and improvement of sensitivity computation using the area-fraction weighted fixed grid FEM and structural optimization. Finite Elem Anal Des 47:933–941

    Article  Google Scholar 

  • Dunning PD, Kim HA (2013) A new hole insertion method for level set based structural topology optimization. Int J Numer Methods Eng 93(1):118–134

    Article  MathSciNet  Google Scholar 

  • Gao T, Zhang W, Duysinx P (2012) A bi‐value coding parameterization scheme for the discrete optimal orientation design of the composite laminate. Int J Numer Methods Eng 91(1):98–114

    Article  MATH  Google Scholar 

  • Ghiasi H, Fayazbakhsh K, Pasini D, Lessard L (2010) Optimum stacking sequence design of composite materials part II: variable stiffness design. Compos Struct 93:1–13

    Article  Google Scholar 

  • Gürdal Z, Olmedo R (1992) Composite laminates with spartially varying fiber orientations: variable stiffness panel concept, AIAA/ASME/ASCE/AHS/ASC 33rd structures, structural dynamics and materials conference, Apr. 13–15, 1992. Dallas, TX, USA

  • Gürdal Z, Olmedo R (1993) In-plane response of laminates with spartially varying fiber orientations: variable stiffness concept. AIAA J 31(4):751–758

    Article  MATH  Google Scholar 

  • Gürdal Z, Haftka RT, Hajela P (1999) Design and optimization of laminated composite materials. Wiley

  • Hammer VB, Bendsøe MP, Lipton R, Pedersen P (1997) Parametrization in laminate design for optimal compliance. Int J Solids Struct 34(4):415–434

    Article  MATH  Google Scholar 

  • Huang J, Haftka RT (2005) Optimization of fiber orientations near a hole for increased load-carrying capacity of composite laminates. Struct Multidiscip Optim 20(5):335–341

    Article  Google Scholar 

  • Keller D (2010) Optimization of ply angles in laminated composite structures by a hybrid asynchronous parallel evolutionary algorithm. Compos Struct 92:2781–2790

    Article  Google Scholar 

  • Khani A, Ijsselmuiden ST, Abdalla MM, Gürdal Z (2011) Design of variable stiffness panels for maximum strength using lamination parameters. Compos Part B Eng 42(3):546–552

    Article  Google Scholar 

  • Kim JS, Kim CG, Hong CS (1999) Optimum design of composite structures with ply drop using genetic algorithm and expert system shell. Compos Struct 46(2):171–187

    Article  MathSciNet  Google Scholar 

  • Kim BC, Potter K, Weaver PM (2012) Continuous tow shearing for manufacturing variable angle tow composites. Compos Part A 43:1347–1356

    Article  Google Scholar 

  • Liu B, Haftka RT (2001) Composite wing structural design optimization with continuity constraints. Proceedings of 42nd AISS/ASME/ASCE/AHS/ASC Structures, structural dynamic and materials conference. Seattle WA

  • Lukaszewicz DHAJ, Ward C, Potter KD (2012) The engineering aspects of automated prepreg layup: history, present and future. Compo Part B 43:997–1009

    Article  Google Scholar 

  • Lund E (2009) Buckling topology optimization of laminate multi-material composite shell structures. Compos Struct 91:158–167

    Article  Google Scholar 

  • Luo JH, Gea HC (1998a) Optimal orientation of orthotropic materials using an energy based method. Struct Optim 15:230–236

    Article  Google Scholar 

  • Luo JH, Gea HC (1998b) Optimal bead orientation of 3D shell/plate structures. Finite Elem Anal Des 31:55–71

    Article  MATH  Google Scholar 

  • Nemeth MP, Britt VO, Collins TJ, Starnes JH. (1996) Nonlinear Analysis of the Space Shuttle Super-Lightweight External Fuel Tank, AIAA/ASME/ASCE/AHS/ASC 37th structures, structural dynamics and materials conference, April 15–17 1996, Salt Lake City, UT

  • Osher S, Fedkiw R (2003) Level set methods and dynamic implicit surfaces. Springer, New York

    Book  MATH  Google Scholar 

  • Pedersen P (1989) On optimal orientation of orthotropic materials. Struct Optim 1:101–106

    Article  Google Scholar 

  • Pedersen P (1991) On thickness and orientational design with orthotropic materials. Struct Optim 3:69–78

    Article  Google Scholar 

  • Raju G, Wu Z, Weaver PM (2012) Prebuckling and buckling analysis of variable angle tow plates with general boundary conditions. Compos Struct 94(9):2961–2970

    Article  Google Scholar 

  • Sethian JA (1999) Level set methods and fast marching methods, 2nd edn. Cambridge University Press, New York

    MATH  Google Scholar 

  • Setoodeh S, Abdalla MM, Gürdal Z (2006a) Design of variable–stiffness laminates using lamination parameters. Compo Part B Eng 37(4–5):301–309

    Article  Google Scholar 

  • Setoodeh S, Gürdal Z, Watson LT (2006b) Design of variable-stiffness composite layers using cellular automata. Comput Methods Appl Mech Eng 195(9–12):836–851

    Article  MATH  Google Scholar 

  • Setoodeh S, Abdalla MM, Ijsselmuiden ST, Gürdal Z (2008) Design of varrible stiffness composites panels for maximum buckling load. Compos Struct 87:109–117

    Article  Google Scholar 

  • Sigmund O, Torquato S (1997) Design of materials with extreme thermal expansion using a three-phase topology optimization method. J Mech Phys Solids 4:1037–1067

    Article  MathSciNet  Google Scholar 

  • Stegmann J, Lund E (2005) Discrete material optimization of general composite shell structures. Int J Numer Methods Eng 62:2009–2027

    Article  MATH  Google Scholar 

  • Sun M, Hyer MW (2008) Use of material tailoring to improve buckling capacity of elliptical composite cylinders. AIAA J 46(3):770–782

    Article  Google Scholar 

  • Tatting B, Gürdal Z (2001) Anaylsis and design of tow-steered variable stiffness composite laminates. In: American helicopter society Hampton Roads chapter, structures specialists’ meeting. Williamsburg (VA)

  • Temmen H, Degenhardt R, Raible T (2006) Tailored fiber placement optimization tool. 25th international congress of the aeronautical sciences. Hamburg, Germany

  • Tosh MW, Kelly DW (2000) On the design, manufacture and testing of trajectorial fiber steering for carbon fiber composite laminates. Compos Part A 31:1047–1060

    Article  Google Scholar 

  • van Campen JMJF, Kassapoglou C, Gürdal Z (2012) Generating realistic laminate fiber angle distributions for optimal variable stiffness laminates. Compos Part B 43:354–360

    Article  Google Scholar 

  • Wu KC (2008) Design and Analysis of Tow-Steered Composite Shells Using Fiber Placement. American Society for Composites, 23rd Annual Technical Conference Memphis, TN, Sept 9–11

  • Wu Z, Weaver PM, Gangadharan R, Kim BC (2012) Buckling analysis and optimization of variable angle tow composite plates. Thin-Walled Struct 60:163–172

    Article  Google Scholar 

  • Wu Z, Raju G, Weaver PM (2013) Feasible region of lamination parameters for optimization of variable angle tow composite plates. 54rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. April 8–11, Boston, Massachusetts

  • Wu Z, Raju G, White S, Weaver PM (2014) Optimal Design of Postbuckling Behaviour of Laminated Composite Plates using Lamination Parameters, 55th AIAA/ASMe/ASCE/AHS/SC Structures, Structural Dynamics, and Materials Conference, 13–17 January National Harbor, Maryland

  • Zabinsky ZB, Tuttle ME, Khompatraporn C (2006) Global optimization: Scientific and engineering case studies. In: Printer J D (eds) A case study: composite structure design optimization, chapter 21, 1st edn. Springer

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Acknowledgments

This work was funded by NASA’s Fixed Wing Project under the Fundamental Aeronautics Program.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Bath, Bath, BA2 7AY, UK

    Christopher J. Brampton & H. Alicia Kim

  2. Structural Mechanics and Concepts Branch, NASA Langley Research Center, Hampton, VA, 23681, USA

    K. Chauncey Wu

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  1. Christopher J. Brampton
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  2. K. Chauncey Wu
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  3. H. Alicia Kim
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Correspondence to Christopher J. Brampton.

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Brampton, C.J., Wu, K.C. & Kim, H.A. New optimization method for steered fiber composites using the level set method. Struct Multidisc Optim 52, 493–505 (2015). https://doi.org/10.1007/s00158-015-1256-6

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  • DOI: https://doi.org/10.1007/s00158-015-1256-6

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